The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method
The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method
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DOI：
10.1080/01621459.2017.1294075
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发表时间：
2018-01-01
影响因子：
3.7
通讯作者：
Doucet, Arnaud
中科院分区：
文献类型：
--
作者：
Bouchard-Cote, Alexandre;Vollmer, Sebastian J.;Doucet, Arnaud
目前可用的许多马尔可夫链蒙特卡罗技术依赖于离散时间可逆马尔可夫过程，其过渡内核是Metropolis-Hastings算法的变体。我们探索并推广了最近在物理学文献中引入的替代方案（Peters和de With 2012），其中使用连续时间不可逆分段确定性马尔可夫过程探索目标分布。在Metropolis-Hastings算法中，尝试移动到目标密度较低的区域，相当于比当前状态更高的“能量”，可以以正概率被拒绝。在这种替代方法中，粒子沿着沿着直线围绕空间移动，当面对高能量障碍时，它不会被排斥，但它的路径会通过碰撞这个障碍而被修改。通过使用非齐次泊松过程重新制定该算法，我们利用标准的采样技术来模拟这个马尔可夫过程在广泛的场景感兴趣。此外，当目标分布由仅依赖于状态变量的子集的因子的乘积给出时，诸如与概率图模型相关联的后验分布，该方法可以被修改以通过允许计算上更便宜的“局部”反弹来利用该结构，该“局部”反弹仅涉及与因子相关联的状态变量，而其他状态变量继续演化。在这种情况下，通过利用化学动力学技术，我们提出了几个计算效率高的实现。在实验上，这类新的马尔可夫链蒙特卡罗方案在各种贝叶斯推理任务（包括高维模型和大型数据集）上优于最先进的方法。本文的补充材料可在网上查阅。
Many Markov chain Monte Carlo techniques currently available rely on discrete-time reversible Markov processes whose transition kernels are variations of the Metropolis-Hastings algorithm. We explore and generalize an alternative scheme recently introduced in the physics literature (Peters and de With 2012) where the target distribution is explored using a continuous-time nonreversible piecewise-deterministic Markov process. In the Metropolis-Hastings algorithm, a trial move to a region of lower target density, equivalently of higher "energy," than the current state can be rejected with positive probability. In this alternative approach, a particle moves along straight lines around the space and, when facing a high energy barrier, it is not rejected but its path is modified by bouncing against this barrier. By reformulating this algorithm using inhomogeneous Poisson processes, we exploit standard sampling techniques to simulate exactly this Markov process in a wide range of scenarios of interest. Additionally, when the target distribution is given by a product of factors dependent only on subsets of the state variables, such as the posterior distribution associated with a probabilistic graphical model, this method can be modified to take advantage of this structure by allowing computationally cheaper "local" bounces, which only involve the state variables associated with a factor, while the other state variables keep on evolving. In this context, by leveraging techniques from chemical kinetics, we propose several computationally efficient implementations. Experimentally, this new class of Markov chain Monte Carlo schemes compares favorably to state-of-the-art methods on various Bayesian inference tasks, including for high-dimensional models and large datasets. Supplementary materials for this article are available online.